Abstract
We consider ad=2 Ising system with a Kac potential whose mean-field critical temperature is 1. Calling γ>0 the Kac parameter, we prove that there existsc *>0 so that the true inverse critical temperature βcr(γ) > 1 +by 2 log γ-1, for anyb<c * and γ correspondingly small. We also show that if γ→0 andb→c *, suitably, then the correlation functions (normalized and rescaled) converge to those of a non-Gaussian Euclidean field theory.
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Communicated by J. L. Lebowitz
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Cassandro, M., Marra, R. & Presutti, E. Corrections to the critical temperature in 2D Ising systems with Kac potentials. J Stat Phys 78, 1131–1138 (1995). https://doi.org/10.1007/BF02183705
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DOI: https://doi.org/10.1007/BF02183705